1. Introduction
In recent years, the network scale of HSR has developed rapidly, and the length of the HSR line also increased. More and more passengers are choosing to travel by HSR. As the number of HSR passengers has increased, some new operational requirements have emerged. In normal times, the demand for passengers to travel by HSR does not fluctuate much. However, the demand fluctuates because of holidays or special activities. Train timetables are designed to meet the travel demands of passengers, which state the departure time and the arrival time of all train operation lines. HSR operation departments need to change the HSR train timetable in time to respond to the travel demands of passengers. Timely adjustment of the timetable according to the number of passengers can make the arrangement of the operation department more aligned with the demands of passengers, and save the cost of operating a railway line for the operation department. The train timetable contains relevant operational plans, such as train-set circulation plans. The train-set circulation plan is a part of the train timetable, which is a detailed plan of how to use the train-sets when implementing the timetable. The schematic diagram of train-set circulation plan is shown in
Figure 1.
As shown in
Figure 1, there are four train operation lines in the timetable, representing four operation tasks. A train-set can only perform one operation at a time. Train-set 1 performs operation line 1 first, and train-set 2 performs operation line 2. After the completion of one operation line, the train needs a period to replenish materials and clean the carriage, to perform the next operation line. This period is called the turn-back time. We can see that one train-set can perform multiple tasks in one day. Train-set 1 will perform operation line 4 after completing operation line 1. Similarly, train-set 2 will perform operation line 3 after completing operation line 2. As a result, a timetable requires fewer train-sets than the operation lines it contains. Such a plan containing the corresponding relationship between train-set and operation line is called a train-set circulation plan. Passengers need to get on or off the train, so, train-set needs to stop at a station to serve passengers. If a train-set does not stop at the station, we call the train-set pass through the station.
When the old timetable is switched to the new timetable, the operation plan related to the timetable also needs to be switched. For the operation department, the number of train-sets required by each station to implement the new timetable may be different from the old timetable. This means that in terms of the location of the train-set, each station has two states. The state after the implementation of the old timetable is the old state, and the state required by the implementation of the new timetable is called the new state. The schematic diagram of the old state and the new state is shown in
Figure 2.
In
Figure 2 we can see that in the old state, station A has two train-sets and station G has three train-sets. However, in the new state, station A needs three train-sets and station G only needs two train-sets. The time between the end time of the old timetable and the start time of the new timetable is called transition time. To meet the number requirement of train-sets in each station in the new timetable, the operation department has two methods. The first is to use spare train-sets to perform operation lines (method 1). Second, at the end of the day, trains will be transferred from nearby stations that have more train-sets to those that lack them (method 2). The schematic diagram of the timetable switching method is shown in
Figure 3.
Figure 2.
The schematic diagram of the old state and the new state.
Figure 2.
The schematic diagram of the old state and the new state.
Figure 3.
The schematic diagram of the timetable switching method.
Figure 3.
The schematic diagram of the timetable switching method.
As shown in
Figure 3, there is a spare train-set in station G and station A is short of a train-set. To make up for this train-set, the backup train-set at station A can be used, or the spared train-set can be transferred from station G to station A during the transition time. The advantage of the first method is that the train does not need to run empty after the end of the operation, so, it will not result in an increase in operating costs and the waste of resources. The disadvantage is that it will occupy the standby train, which will affect the robustness of the timetable in the implementation process. If there is an emergency, the number of standby train-set may be insufficient, which will expand the negative impact. The advantage of the second method is that it will not affect the robustness in the timetable implementation process, but the disadvantage is as mentioned above, which will cause the waste of resources.
In the past, the train timetable was adjusted infrequently, perhaps only a few times a year. Under this adjustment frequency, there is little difference between the two methods. However, as the number of passengers who chose to travel by HSR increased significantly, the fluctuation range of the number of passengers has increased too. In this case, the previous operation mode of only changing the timetable a few times a year has a large lag relative to passenger travel demands. In order to meet the travel demands of passengers better and save the cost of the operation department, it is necessary to increase the adjustment frequency of the train timetable. The increase in the frequency of train timetable adjustment will amplify the disadvantages of the above two modes, resulting in increased waste of resources or greatly affecting the robustness in the process of timetable implementation.
How to avoid the disadvantages of the above two methods and meanwhile scheduling the train-sets, is a problem that is worth studying, because saving resources while meeting the travel demands of passengers is of great significance for practical applications. Thus, we proposed an approach to extend the transition time. In this approach, we extend the transition time from a few hours to a day and realize the train-set rescheduling from the old state to new state through a one-day operation. We call the operation plan during the transition time the transition timetable. The transition timetable proposed in this paper is an approach for the HSR operation department to transition from the old timetable to the new timetable through the operation. The new timetable and the old timetable have been determined by the operation department. The transition timetable scheduling is a train timetabling problem (TTP), and the relevant train-set circulation plan scheduling is a train-set rescheduling problem (TRP). In the scenario proposed in this paper, the TRP has a higher priority, to avoid the disadvantages of the above two methods.
Both train timetabling problem (TTP) and train-set rescheduling problem (TRP) are complex for long distance HSR lines:
Firstly, train timetables are designed to meet the travel demands of passengers. For the long distance HSR line, the passenger travel demands are more complex. The demand that passengers travel from the origin station to the destination station is called O-D. For example, the number of types of O-D for an HSR line with six stations is:
Let
be the quantity of stations of the HSR line, the number of O-D types is:
Obviously, with the increase in the quantity of stations along the HSR line, the types of O-D increase too. For the long distance HSR line, there are more than twenty stations and there will be more than 300 types of O-D.
Secondly, there are more passengers on the long distance HSR line. The operation department needs to prepare more train-sets to meet the travel demands of passengers. Thus, the complexity of scheduling a train-set circulation plan is higher than a normal railway line.
Thirdly, due to the increasing adjustment frequency of timetables, the requirement of solving efficiency is higher than that of the past. However, the TRP and the TTP are more difficult to solve due to the scale of the problem in long distance HSR lines.
In the normal approach, a train timetable is scheduled at first, to meet the passenger travel demands. Then the train-set circulation plan is scheduled according to the timetable. The disadvantage is, as mentioned above, that it leads to a waste of resources. Moreover, if the operation department only adjusts the timetable to meet the new state requirements, it will affect the satisfaction of passenger travel demands too. It is very difficult to solve the train timetable and the train-set circulation plan directly at the same time because the scale of the problem is too huge for long distance HSR lines and the time consumption will be unacceptable. The approach proposed in this paper aims to meet the demands of passengers as much as possible, without affecting the robustness of the implementation of the new timetable, and avoid the waste of resources. We calculated the train-set circulation plan and stop plan respectively, and finally matched them to obtain the timetable. The scale of each problem is smaller than the overall problem, which is easy to solve. The approach framework used in this paper is shown in
Figure 4.
As shown in
Figure 4, we need the structure of the HSR, the operation safety parameters of the HSR, the position of the train-sets in the new state and the old state, and the travel demand of passengers before scheduling the transition timetable and the train-set circulation plan.
The first step is to calculate the primary train-set circulation plan according to the position and state data of the train-set, the structure of the HSR and the operation safety parameters. We established a profit function according to the full load ratio of trains in different sections. The higher the load rate of the train, the higher the profit. Based on the profit function, we build an integer programming model with profit maximization as the goal and use CPLEX to solve. The plan obtained in this step is called the primary train-set circulation plan, which will be used in the third step to match with the stop plan.
The second step is to calculate the stop plan according to the structure of HSR, operation safety parameters and passenger travel demands. The calculation of the stop plan should be based on the service plan. If a train arrives, departs, or passes through a station, we call the train serves the station. In the service plan, we define the minimum quantity of trains that stop at each station. Moreover, the quantity of trains is calculated by decomposing the passenger travel demands. The stopping plan here is used to match the train-sets of the primary train-set circulation plan.
The third step is to match the primary train-set circulation plan and stop plan, based on a genetic algorithm (GA). In order to save time, we calculate the train timetable according to the operation safety parameters after the matching scheme is obtained by the GA. We adjust the operation lines beyond the operating time range, to output the final timetable and the train-set circulation plan that meets the operational requirements.
The main contributions of this paper to the study of the TRP and the TTP are as follows:
An integer programming model based on profit function was designed, and CPLEX was used to solve the primary train-set circulation plan in a very short time.
Based on the decomposition method of passenger travel demands, the service plan is constructed. We use CPLEX to solve the model and obtain the stop plan.
We proposed a GA to calculate the matching relationship of the primary train-set circulation plan and the stop plan, then calculate and adjust the timetable according to the safety operating requirements.
The rest of the paper is as follows: In the second section, we summarize the existing research. In the third section, we describe the construction method of the train-set section sequence and the profit function of it and establish the integer programming model for scheduling the primary train-set circulation plan. In the fourth section, we describe the decomposition method of passenger travel demands, which can convert the complex passenger travel demands into a service plan. Then, we introduce a method to calculate the stop plan based on the service plan. In the fifth section, we propose a GA to match the primary train-set circulation plan and the stop plan. Moreover, we design an adjusting method of the plan and timetable, to make them meet the operating requirements. In the sixth section, we carry out a real-world case study on the Beijing-Shanghai HSR. We analyzed the performance of the approach from the perspective of the application. In the seventh section, we summarize the paper and present the recommendations for further research.
7. Conclusions
In this paper, an approach is proposed to solve the problem of scheduling the timetable and train-set circulation plan under the frequency switching scenario of the timetable. This approach considers the travel demands of passengers and the operational requirements of HSR. It can save the cost of railway operation department while realizing the state changing of train-set during the transition time.
Firstly, we design an inter programming model including section sequence for train-set, so that the operating distance can be decided based on each section’s operating profits. We use CPLEX to solve the model in a very short time. By this model, we obtained a maximum benefit oriented primary train-set circulation plan, which will be matched with the stop plan.
Secondly, we design a method for solving the stop plan based on passenger travel demands. For the passenger travel demands, we adopted the travel demands decomposition method to covert the complex passenger travel demands into the service plan. Then we use CPLEX to calculate the stop plan according to the service plan efficiently.
Thirdly, we design the matching and adjusting method of the stop plan and the primary train-set circulation plan. In the method, we split the primary train-set circulation plan into different schemes at first. Then we match the schemes in the stop plan and the schemes in the train-set circulation plan by a customized GA we designed. After one-to-one correspondence is determined between the schemes in the stop plan and schemes in the primary train-set circulation plan, the timetable can be calculated. Finally, the final train-set circulation plan and timetable are obtained.
Fourthly, we test the approach we proposed by the Beijing-Shanghai HSR. The results show that for the aspect of passenger travel demands, the approach proposed in this paper can meet 94.61% of passenger travel demands, and the solving efficiency is higher than the normal approach. What is more, it can save the costs of the operation department.
In the future, we will continue to take the practical application as the guidance to study the collaborative scheduling of timetable and train-set circulation plan:
Firstly, some other algorithms can be used to improve the solving efficiency. We will try to use gradient methods and compare the solving efficiency and the quality of solutions between different algorithms.
Secondly, as there are always some stochastic effects that affect railway traffic, we will optimize the reserve deposit between train intervals to balance the railway traffic efficiency and robustness. Moreover, also, we need to study how to recover normal operation order as soon as possible after disturbance.
Thirdly, we will consider adding the maintenance mileage of the train into the model, which is urgently needed in practical applications. The maintenance of the train may affect the scheduling of the circulation plan of the train-set because, under the existing train-set utilization system, the train-set needs to be checked and repaired at specific locations, which may affect the stop position of the train.